${\sqrt[3]{512} = \text{?}}$
Explanation: $\sqrt[3]{512}$ is the number that, when multiplied by itself three times, equals $512$ If you can't think of that number, you can break down $512$ into its prime factorization and look for equal groups of numbers. So the prime factorization of $512$ is $2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$ We're looking for $\sqrt[3]{512}$ , so we want to split the prime factors into three identical groups. Notice that we can rearrange the factors like so: $512 = 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2 = \left(2\times 2\times 2\right)\times\left(2\times 2\times 2\right)\times\left(2\times 2\times 2\right)$ So $\left(2\times 2\times 2\right)^3 = 8^3 = 512$ So $\sqrt[3]{512}$ is $8$.